Lesson 6 Magnetic field induced transport in nanostructures.

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Presentation transcript:

Lesson 6 Magnetic field induced transport in nanostructures

- Short review of the effects of a magnetic field on an electron in bulk system - Effects of a magnetic field on an electron in 0D, 1D, 2D nanostructures (modification of the density of states!!) - Quantization of the magnetic flux - Quantum Hall effect

A) Effect of a uniform magnetic field on a crystal

Free electrons in y and z. Confined electrons in x (by harmonic potential) Landau Levels

Key consequence: Changing the electrons density of states n 3D  n 1D Landau Levels

n 3D  n 1D General effect of a magnetic field on the electrons density of states: restriction by 2 dimensions n 2D  n 0D B) Low dimensional systems in magnetic fields 2D 0D

C) Density of states of a 2D system in a magnetic field (Towards the quantum Hall effect)

D) The Aharonov-Bohm effect: evidence for the magnetic flux quantization L  >>L, B  0  Electrons interference effects

Webb experiment to prove the Aharonov-Bohm effect

E) 2D system in a magnetic field: Landau levels and filling factor

42 2

F) The quantum Hall effect - Classical Hall effect

Quantum Hall effect - Experimental facts and elementary theory of integer quantum Hall effect Low-Dimensional semiconductor (ex. 2DEG)

R xx R xy =R H

R K =h/e 2 von Klitzing constant (quantum of resistance)

n=